Robert Cullen, Lord Cullen FRSE (1742–1810) was a Scottish judge. He played a key role, along with his father William Cullen, in obtaining a royal charter for the Philosophical Society of Edinburgh, resulting in the formation of the Royal Society of Edinburgh in 1783.
Born on 22 September 1742, in Edinburgh, the son of eminent physician and chemist William Cullen and Anne Johnstone (d.1786). His brother was the physician Henry Cullen. The family lived at Mint Close on the Canongate, home of the old Scottish Mint.
Robert was educated at the High School and then Edinburgh University. He was admitted to the Faculty of Advocates in 1764, and served as a Senator of the College of Justice (1796-9), and as Lord of Justiciary (1799–1810).
In 1783 he was a joint founder of the Royal Society of Edinburgh.
He died on 28 November 1810 and was buried in Kirknewton churchyard, south-west of Edinburgh.
He was married to Mary Russell who died in 1818. They had no children.